{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Logistic Regression MAP classifier\n",
    "==\n",
    "## Simon Rogers, Feb 2017"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pylab as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Generate some data with two classes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "x = np.random.randn(50,2)\n",
    "x[:25,:] += 1.5\n",
    "x[25:,:] += -1.5\n",
    "t = np.zeros((50,1))\n",
    "t[25:] += 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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pUj4/rWJx32Wfy+VOqbf31hhahUa0diZ3pR/sJF/0tuLMiRMavcIQwJGpqYae1Nbc3KzR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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x109fae7d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "styles = ['ro','bo']\n",
    "classes = np.unique(t)\n",
    "for i,classn in enumerate(classes):\n",
    "    pos = np.where(t==classn)[0]\n",
    "    plt.plot(x[pos,0],x[pos,1],styles[i])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use Newton-Raphson to find the $\\mathbf{w}$ that maximises the likelihood"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "sig_sq = 0.5 # prior variance for w (assuming mean zero)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def grad_function(w,x,t,sig_sq):\n",
    "    P = 1.0/(1.0 + np.exp(-np.dot(x,w)))\n",
    "    return (-1.0/sig_sq)*w + np.dot(x.T,t-P)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def hess_function(w,x,t,sig_sq):\n",
    "    P = 1.0/(1.0 + np.exp(-np.dot(x,w)))\n",
    "    P = P.flatten() # required for the diagonalisation\n",
    "    return -(1.0/sig_sq)*np.eye(len(w)) - np.dot(x.T,np.dot(np.diag(P*(1-P)),x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "w = np.zeros((2,1)) # Initial guess\n",
    "\n",
    "all_w = []\n",
    "all_w.append(w.flatten())\n",
    "for it in range(10):\n",
    "    w = w - np.dot(np.linalg.inv(hess_function(w,x,t,sig_sq)),grad_function(w,x,t,sig_sq))\n",
    "    all_w.append(w.flatten())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the convergence of the w values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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/mNnvZpZhZr39qjEa/P3vULMmXH998fvc1uE22h/Znv4v92fTjk3+FSciIjHD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\niEjIFChEREQkZP8PXW13MvNasfoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a320710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "all_w = np.array(all_w)\n",
    "for i in range(2):\n",
    "    plt.plot(all_w[:,i])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the decision boundary. We will actually plot probability contours by making a big grid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "gridX,gridY = np.meshgrid(np.arange(-5,5,1),np.arange(-6,5,1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "P = np.zeros_like(gridX,dtype=np.float)\n",
    "for i,row in enumerate(gridX):\n",
    "    for j,val in enumerate(row):\n",
    "        pos_vec = np.vstack((val,gridY[i,j]))\n",
    "        P[i][j] = (1.0/(1+np.exp(np.dot(-w.T,pos_vec))))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.contour.QuadContourSet at 0x10a792850>"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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G5yQ9ozphw/fkYxR52cJDWhPEBR1uLADqeIDfZNPTgA8HwaI/dAmbYHZ2Nowc+RG7d3fi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\nIYQQTubfeoo/YKQIgGQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a7aebd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "for i,classn in enumerate(classes):\n",
    "    pos = np.where(t==classn)[0]\n",
    "    plt.plot(x[pos,0],x[pos,1],styles[i])\n",
    "plt.contour(gridX,gridY,P)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
